Some endoscope sheaths include one or more features, such as a sheath tube tip, for cleaning a distal viewing end of an endoscope or for providing illuminating functions, viewing functions, or both to the distal viewing end of an endoscope and/or an internal location of a patient. To function properly, the sheath tube tip may need to be generally rotationally aligned with the distal viewing end of the endoscope, the internal location of the patient, or both. Some endoscope sheaths include a specific detail, such as an arm, configured to engage another specific detail on the endoscope like a light post. This type of engagement not only provides a connection means between the endoscope sheath and the endoscope, but also rotationally aligns the sheath tube tip and the distal viewing end. However, in some instances, the position of the light post may vary, which may, accordingly, affect the rotational alignment between the sheath tube tip and the distal viewing end of the endoscope, the internal location of the patient, or both. For example, in some instances, the light post can extend from the endoscope in different directions (e.g. the light post can extend upwardly or downwardly from the endoscope), which may affect the rotational alignment between the sheath tube tip and the distal viewing end of the endoscope, the internal location of the patient, or both. In these instances, to achieve rotational alignment there between, various individual endoscope sheath configurations may be required for engaging various individual endoscope configurations which may undesirably increase endoscope sheath inventory, increase the space required to store the increased endoscope sheath inventory, and also increase the time required to prepare for a medical procedure, for example. In other instances, for example, depending on how a doctor holds the endoscope, the light post can be made to extend upwardly, downwardly, or in a different direction, which may also affect the rotational alignment of the sheath tube tip relative to the internal location of the patient. What is needed is a single endoscope sheath that can engage an endoscope with an upwardly extending light post, a downwardly extending light post, or a light post extending in a direction in between, while providing for the sheath tube tip to be rotationally adjusted relative to the distal viewing end of the endoscope, an internal location of a patient, or both. Some examples of endoscope sheaths can be found in U.S. Pat. Nos. 7,811,228, 5,554,112, and 5,797,836; U.S. Pat. Pubs. 2013/0205936 and 2002/0120180; and U.S. patent application Ser. Nos. 14/493,700 and 14/493,581, all of which are incorporated by reference herein in their entirety for all purposes.